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Beliebt Rechnen >

(\partial)/(\partial x)(5xye^{-x^2y})

Lösung

\frac{\partial}{\partial x} (5 x y e^{- x^{2} y})

Lösung

5 y (e^{- x^{2} y} - 2 e^{- x^{2} y} x^{2} y)

Schritte zur Lösung

\frac{\partial}{\partial x} (5 x y e^{- x^{2} y})

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 y \frac{\partial}{\partial x} (x e^{- x^{2} y})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{- x^{2} y}

= 5 y (\frac{\partial}{\partial x} (x) e^{- x^{2} y} + \frac{\partial}{\partial x} (e^{- x^{2} y}) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (e^{- x^{2} y}) = - 2 y e^{- y x^{2}} x

= 5 y (1 \cdot e^{- x^{2} y} + (- 2 y e^{- y x^{2}} x) x)

Vereinfache

5 y (1 \cdot e^{- x^{2} y} + (- 2 y e^{- y x^{2}} x) x) : 5 y (e^{- x^{2} y} - 2 e^{- x^{2} y} x^{2} y)

= 5 y (e^{- x^{2} y} - 2 e^{- x^{2} y} x^{2} y)

Beliebte Beispiele

limit as x approaches infinity of (0)^x

x \to \infty lim ((0)^{x})

derivative of (2/(x^3)^2)

\frac{d}{d x} ((\frac{2}{x ^{3}})^{2})

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\int cot (22 x) d x

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\int (x^{2} + x + 1) (e^{x}) d x

limit as x approaches 0 of 3x-5

x \to 0 lim (3 x - 5)